Inference for One Variance: An Example of a Confidence Interval and a Hypothesis Test

I work through an example of a confidence interval and a hypothesis test for a variance (using chi-square methods that are appropriate when sampling from a normally distributed population).
The cereal data is from a sample of 15 bags of cereal that I collected and weighed.
I have a video introduction to these procedures available at: • An Introduction to Inf...

[@hovhadovah]

I love how clearly you articulate everything. It makes it much easier to understand what you're teaching. Thanks for the effort! My instructor made this much harder than it apparently is.

[@jbstatistics]

Thanks for the kind words!

[@TheKhushty]

Your videos are brilliant…surprised you don't have hundreds of thousands of views!!! Keep up the great work, such a good teacher!!!

[@jbstatistics]

Thanks for the compliments! I'll definitely be making more videos. Cheers.

[@Cleisthenes2]

I don't really understand why one hypothesis is that the variance is less than 5, and another is that it is exactly 5. Why not more than 5?

[@yasinzamani9467]

Shouldn't "upper one-sided" confidence interval for sigma be calculated instead of "two-sided"?!

[@jbstatistics]

I think that in the vast majority of circumstances, a two-sided interval is more useful. I carried out a one-sided test here, but that doesn't mean I can't also find a two-sided interval. I barely mention the notion of one-sided intervals in my intro stats courses.

[@yiwenzheng3129]

very good videos, just one minor thing that population variance is not a random variable, it's an unknown constant, it might be uncomfortable to state that the the population variance lies within this interval, i think it will be more accurate to say if we carry the same statistical procedure for 100 times, then approximately 95% of the confidence intervals will capture the population variance.

[@jbstatistics]

Thanks for the feedback, but nowhere in here do I imply that the population variance is a random variable. A constant can lie within an interval. I have detailed discussions of interpretation of confidence intervals in other videos, and while I discuss the repeated sampling argument there, I don't believe it's the best way to explain a single given interval in a practical setting. Cheers.

[@add1son]

why do we use a chi squared distribution?

[@katiejom80]

Agreed! Thanks for your help!

[@Ahmed-jl7uh]

This video is so comprehensive, it made me better understand the concepts of Hypothesis testing, Critical Value, Confidence Interval etc. even though this video is slightly advanced but it does a good job bringing up all the basic concepts accompanied with a practical real-life example. Thanks!

[@ugyennorbu9443]

I download the videos for future reference and safe keeping. Maybe that why it does not have much views. But this shows bogus view counts dont always translate to quality.

[@saurabhagrawal3934]

You have very nicely explained these advanced topics. Please make a video on PCA and applications.

[@ugyennorbu9443]

I would like to request you to make videos on estimation theory in statistics if your schedule permits.
Thank you so much.

[@UlisUlis-ep1lj]

Thank you for the video! I didn't get where such value of "s" comes from though. Can you please clarify that?

[@UlisUlis-ep1lj]

our variance is 5 and the square root of 5 is 2.23, not 2.83. I'm so confused!

[@vikadot1998]

thank you for you help!

[@jbstatistics]

You are very welcome!